Jeremy Corbyn has said Theresa May should pay a price in Thursday’s general election for ignoring “repeated warnings” not to cut police numbers.
The Labour leader said Mrs May had “presided” over a 19,000 fall in numbers as home secretary and he agreed with those calling on her to resign in the wake of the London Bridge attacks.
But the PM said she had protected counter-terror police numbers.
And she accused the Labour leader of opposing shoot-to-kill powers.
With less than 72 hours to go before Thursday’s election, party leaders have returned to the campaign trail after electioneering was briefly suspended because of the London Bridge attack, in which seven people died.
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Following a meeting of senior ministers and security chiefs at the emergency Cobra committee, Mrs May said Saturday’s atrocity was an attack on “the free world” and said she was best equipped to deal with the “evolving” threat facing the UK.
In a speech in London, she vowed to tackle the “whole spectrum” of extremism as security took centre stage in the election.
Action was needed in communities and online to ensure “bigotry and hatred” did not turn to violence, the PM said.
She defended her record on security over the past seven years in the face of criticism that she had presided, as home secretary, over a fall of more than 19,000 in police numbers between 2010 and 2016 and accused officers of “crying wolf” over their capabilities.
She said she had protected counter-terror police budgets as home secretary and was now “providing funding for an uplift in the number of armed officers” as well as protecting funding for the police as a whole.
Saying leadership was “absolutely vital” for keeping the UK safe, she said Mr Corbyn had “boasted” of opposing every single piece of counter-terrorism legislation and had voiced his opposition to shoot-to-kill powers, saying the response of the police to Saturday’s attack showed how vital these were.
But Mr Corbyn suggested the government’s decision to cut police numbers by 19,000 between 2010 and 2016 was now coming back to haunt Mrs May.
Asked whether he agreed with a call by some, including former Downing Street adviser Steve Hilton, for Mrs May to quit, he said he did, but added that the “best way” for the issue to be dealt with was by voters on Thursday.
In the first of a whirlwind series of campaign events planned for the next 72 hours Mr Corbyn said of the terrorists: “We are not going to allow them to dictate how we live or how we go about enjoying themselves. We carry on and our democracy will prevail.”
Analysis – BBC political editor Laura Kuenssberg
Voters choose their political parties for all sorts of different reasons. But as this strange election hurtles towards its close, the demand of who can keep the country safe is firmly on the table.
For Theresa May that doesn’t just mean questions over how she would counter extremism if she stays in power. She faces criticism too over the Tories’ record on squeezing money for the police.
Labour leader Jeremy Corbyn has repeated his promise to reverse the cuts and slammed the Tories, warning the government could not “protect the public on the cheap”.
He also tried to counter perceptions that he is soft on security, including his earlier stance on shoot-to-kill, which he questioned days after the Paris attack at the Bataclan. He said, if he were prime minister he would take “whatever action is necessary and effective” to protect the public.
After a brief pause, the election campaign is well and truly back, even if with a more subdued tone, and with security as its primary subject.
Lib Dem leader Tim Farron has accused the Conservatives of making the “wrong choices” over police budgets, “posturing” over internet surveillance powers and not putting enough pressure on allies in the Middle East to turn the screw on extremist groups.
“Fewer police on the beat means fewer conversations, less information being passed on and less knowledge about who’s who and who needs to be kept under surveillance,” he wrote in an article for the Guardian.
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He added: “Theresa May talks of the need to have some difficult and sometimes embarrassing conversations. That should include exposing and rooting out the source of funding terror, even if it means difficult and embarrassing conversations with those like Saudia Arabia that the government claims are our allies.”
He warned about the UK seeking to “control” the internet in a manner associated with regimes like North Korea. “If we turn the internet into a tool for censorship and surveillance, the terrorists will have won. We won’t make ourselves safer by making ourselves less free.”
On Sunday the PM called for new measures to tackle extremism – including online – saying in a speech outside No 10 that “enough is enough”.
Culture Secretary Karen Bradley told the BBC that the fight against online radicalisation meant getting “access to information as required” from tech firms.
Pressed on whether this meant penetrating encrypted messaging services, she said the tech industry had done the “right thing” in the past in terms of removing indecent images from their platforms and now ministers wanted the “same response” over extremist material.
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“We know it can be done and the internet companies want to do it,” she told BBC Radio 4’s Today.
Appearing on a Question Time general election special on Sunday night, UKIP leader Paul Nuttall called for 20,000 more police officers on UK streets, and for a review of funding of mosques in Britain while Green Party co-leader Jonathan Bartley said the Prevent counter-radicalisation strategy should be scrapped.
SNP leader and Scottish first minister Nicola Sturgeon has said it makes sense to review counter-terror arrangements following the latest attacks but that no community should be made a scapegoat for the actions of a “mindless minority”.